Question

What are the intercepts of `3x+2y=14`?

Answer 1

The intercepts are at
`color(white)("XXX")(0,7)` (the y-intercept)
and
`color(white)("XXX")(14/3,0)` (the x-intercept)

Explanation:

For all values on the Y-axis: `x=0`
Replacing `x` with `0` in the given equation:
`color(white)("XXX")3(0)+2y=14`

`color(white)("XXX")rarr y=7`
So the y-intercept is `7` (i.e. it is at `(0,7)`)

For all values on the X-axis: `y=0`
Replacing `y` with `0` in the given equation:
`color(white)("XXX")3x+2(0)=14`

`color(white)("XXX")rarr x= 14/3`
So the x-intercept is `14/3` (i.e. it is at `(14/3,0)`)